Given the following partial dp array after processing coins [1, 2] for amount=5: dp = [1, 1, 2, 2, 3, 3] What is the next coin denomination added if the final dp array after processing all coins is [1, 1, 2, 2, 3, 4]?

hard🔄 Reverse Engineer Q9 of Q15

Dynamic Programming: Knapsack - Number of Ways to Make Change

ACoin 3

BCoin 5

CCoin 4

DCoin 6

Step-by-Step Solution

Solution:

Step 1: Analyze dp before last coin
dp[5] = 3 means 3 ways to make 5 using coins [1,2].
Step 2: Analyze dp after last coin
dp[5] = 4 means one additional way added by last coin.
Step 3: Identify coin that adds one new way to make 5
Coin 5 adds dp[5-5]=dp[0]=1 way, increasing dp[5] by 1.
Final Answer:
Option B -> Option B
Quick Check:
Only coin 5 can add exactly one new way at amount 5 [OK]

Quick Trick: Check dp increments at amount to identify coin added [OK]

Common Mistakes:

MISTAKES

Choosing coin that doesn't fit amount
Ignoring dp state meaning
Assuming multiple coins added

Trap Explanation:

PITFALL

Candidates often guess coin values without reasoning dp increments.

Interviewer Note:

CONTEXT

Tests deep understanding of dp state transitions and reverse reasoning.

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More Dynamic Programming: Knapsack Quizzes

Given the following partial dp array after processing coins [1, 2] for amount=5: dp = [1, 1, 2, 2, 3, 3] What is the next coin denomination added if the final dp array after processing all coins is [1, 1, 2, 2, 3, 4]?

Step 1: Analyze dp before last coin

Step 2: Analyze dp after last coin

Step 3: Identify coin that adds one new way to make 5

Final Answer:

Quick Check:

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